Question: Solve for $x$ and $y$ using elimination. ${5x-3y = 4}$ ${3x+3y = 36}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3y$ and $3y$ cancel out. $8x = 40$ $\dfrac{8x}{{8}} = \dfrac{40}{{8}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {5x-3y = 4}\thinspace$ to find $y$ ${5}{(5)}{ - 3y = 4}$ $25-3y = 4$ $25{-25} - 3y = 4{-25}$ $-3y = -21$ $\dfrac{-3y}{{-3}} = \dfrac{-21}{{-3}}$ ${y = 7}$ You can also plug ${x = 5}$ into $\thinspace {3x+3y = 36}\thinspace$ and get the same answer for $y$ : ${3}{(5)}{ + 3y = 36}$ ${y = 7}$